# Math Help - Kern and Bland Solid Mensuration problem 18 pg8

1. ## Kern and Bland Solid Mensuration problem 18 pg8

Each of the four circles shown in the figure above is tangent to the other three.
(a) If the radius of each of the smaller circles is a, find the area of the largest circle.
(b) If a = 2.71 what is the area of the largest circle?

2. Originally Posted by cutiemike1

Each of the four circles shown in the figure above is tangent to the other three.
(a) If the radius of each of the smaller circles is a, find the area of the largest circle.
(b) If a = 2.71 what is the area of the largest circle?

connect the centers of the three smaller circles, which forms an equilateral triangle with side length $2a$.

height of this equilateral triangle (which is also a median) is $a\sqrt{3}$

the centroid of the equilateral triangle is the center of the large circle ... you need to calculate the distance along the median from the triangle's vertex to the centroid, and add that distance to $a$ to get the large circle's radius.

recall the ratio that a centroid divides a median.

3. Originally Posted by cutiemike1

Each of the four circles shown in the figure above is tangent to the other three.
(a) If the radius of each of the smaller circles is a, find the area of the largest circle.
(b) If a = 2.71 what is the area of the largest circle?

... as usual I'm too late with my answer. So I only post the sketch which illustrates skeeter's way of solving your question.

4. earboth ... what are you using to make such a nice diagram?

5. Originally Posted by skeeter
earboth ... what are you using to make such a nice diagram?
Guten Abend,

have a look here: euklid dynageo homepage

1. It's more or less the standard software in German schools to do geometric constructions.
2. It is a dynamic program that means you are able "to pull" at points or line segments and watch how the figure is changed.
3. You can "record" the path of a point if you change the property of a drawing (see attachment)
4. The program costs some €.
5. I don't know if there is an English version available.

6. You can use the program as a shareware version but (I believe) you can't save your constructions.

If necessary contact me for further informations by pm.

6. .i'm very sorry sir, i get the idea of how to do it, but i don't know how to get the centroid of a triangle and its median.

7. Originally Posted by cutiemike1
.i'm very sorry sir, i get the idea of how to do it, but i don't know how to get the centroid of a triangle and its median.
then you have something to research on your own. try googling triangle centroid.

8. Originally Posted by skeeter
then you have something to research on your own. try googling triangle centroid.
i researched about the triangle centroid and what i can only find out is the centriod of a right triangle. now, should i multiply it by 2 because it's equilateral triangle? so it will become 2(a+b+c)/3 ?

9. The centroid of a triangle divides each one of its medians in the ratio 2:1